Environ. Sci. Technol. 2008, 42, 4676–4682
An Assessment of Fecal Indicator Bacteria-Based Water Quality Standards A N D R E W D . G R O N E W O L D , * ,† MARK E. BORSUK,‡ R O B E R T L . W O L P E R T , †,§ A N D KENNETH H. RECKHOW† Nicholas School of the Environment, Duke University, Durham, North Carolina 27708, Thayer School of Engineering, Dartmouth College, Hanover, New Hampshire 03755, and Department of Statistical Science, Duke University, Durham, North Carolina, 27708
Received December 16, 2007. Revised manuscript received April 1, 2008. Accepted April 4, 2008.
Fecal indicator bacteria (FIB) are commonly used to assess the threat of pathogen contamination in coastal and inland waters. Unlike most measures of pollutant levels however, FIB concentration metrics, such as most probable number (MPN) and colony-forming units (CFU), are not direct measures of the true in situ concentration distribution. Therefore, there is the potential for inconsistencies among model and sample-based water quality assessments, such as those used in the Total Maximum Daily Load (TMDL) program. To address this problem, we present an innovative approach to assessing pathogen contamination based on water quality standards that impose limits on parameters of the actual underlying FIB concentration distribution, rather than on MPN or CFU values. Such concentration-based standards link more explicitly to human healthconsiderations,areindependentoftheanalyticalprocedures employed, and are consistent with the outcomes of most predictive water quality models. We demonstrate how compliance with concentration-based standards can be inferred from traditional MPN values using a Bayesian inference procedure. This methodology, applicable to a wide range of FIB-based water quality assessments, is illustrated here using fecal coliform data from shellfish harvesting waters in the Newport River Estuary, North Carolina. Results indicate that areas determined to be compliant according to the current methods-based standards may actually have an unacceptably high probability of being in violation of concentration-based standards.
1. Introduction Section 303(d) of the United States Clean Water Act requires that states assess the condition of surface waters and report those which fail to meet ambient water quality standards (1, 2). These are added to the United States Environmental Protection Agency (USEPA) list of impaired waters (3) and can only be removed after the performance of a Total Maximum Daily Load (TMDL) assessment (4, 5) followed by sample-based verification that the standards are being met. The primary objective of a TMDL assessment is to determine * Corresponding author e-mail:
[email protected]. † Nicholas School of the Environment, Duke University. ‡ Thayer School of Engineering, Dartmouth College. § Department of Statistical Science, Duke University. 4676
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the maximum allowable pollutant load from point, nonpoint, and natural sources, including a margin of safety (MOS), which can be discharged into a receiving water without violating water quality standards (2, 4). Such predictive assessments are usually based on an empirical or mechanistic water quality model relating pollutant loading levels to water body concentrations (6, 7). The latest official assessment of U.S. water quality data (8) indicates that pathogens are the leading cause of coastal shoreline standard violations (275 total miles impaired) and the second leading cause of violations in rivers and streams (82,100 total miles impaired). Fecal indicator bacteria (FIB), such as fecal coliform, are commonly used to assess potential pathogen contamination in coastal waters, and concentration estimates are based on indirect measures of microbial density. These are typically reported as either the most probable number (MPN) or the number of colony-forming units (CFU) per unit volume. As a result, MPN- and CFU-based estimates of FIB form the basis of numeric water quality standards for several designated uses including drinking water supply (9), recreational use (10), and shellfish harvesting (11). Unlike most measures of pollutant levels, the probability distributions of MPN and CFU do not directly correspond to the true in situ concentration distribution. The true FIB concentration at a fixed point over time is typically believed to have a continuous unimodal (often log-normal) probability distribution (12, 13). The probability distributions of corresponding MPN and CFU values for the same monitoring location, however, are discrete and, in the case of the MPN, often multimodal. In addition, MPN and CFU variability depends on the number and volume of sample aliquots. Accurately predicting MPN- or CFU-based standard violations from FIB loading levels should therefore involve explicit acknowledgment of how a model-predicted receiving water concentration translates into an MPN or CFU value, and then how frequently those MPN and CFU values violate standards (5, 14). A review of current modeling practice, however, indicates that such an approach is seldom, if ever, implemented. We present a three-part approach to assessing water body impairment from model-based predictions of FIB concentration, using MPN- and CFU-based fecal coliform standards in shellfish harvesting waters as an example. First, we simulate the frequency with which a model-generated distribution of the true FIB concentration c yields MPN and CFU values that violate shellfish harvesting area water quality standards. Second, we identify the distributional parameters of c expected to lead to water quality standard violations no more than a specified percentage of the time (e.g., 10%). We propose that these parameters be used as the basis for FIB-based standards because they do not depend on the analytical method employed, are more closely related to the true water body concentration, and are consistent with the outcomes of most water quality models. In the third part, we demonstrate how compliance with such concentration-based standards can be inferred from traditional MPN and CFU values using a Bayesian approach. We demonstrate this procedure using data from the most recent assessment of shellfish harvesting waters in the Newport River Estuary of Eastern North Carolina. 1.1. Background on Current FIB-Based Water Quality Standards. Model Ordinance in the Guide for the Control of Molluscan Shellfish, prepared by the National Shellfish Sanitation Program (NSSP), includes recommended water quality criteria for shellfish-growing waters based on numeric limits on MPN- and CFU-based measures of fecal coliform 10.1021/es703144k CCC: $40.75
2008 American Chemical Society
Published on Web 05/22/2008
TABLE 1. NSSP Shellfish Harvesting Area Fecal Coliform Water Quality Standards Based on a Minimum of 30 Randomly Collected Samples
2. Methods
standard basis for standard n MPN observations from 5-tube MTF procedure n CFU observations from MF procedure
CFU-based water quality standard violations and associated management decisions. The following section describes our attempt to fill this gap.
q50
µgeo
q90
14
14
43
14
14
31
concentration (11). States which participate in the NSSP, and which are also members of the Interstate Shellfish Sanitation Conference, enforce the Model Ordinance as a minimum requirement for sanitary control of shellfish (11). While similar FIB-based water quality standards are enforced in surface waters with other designated uses, such as recreational use (10) and drinking water supply (9), we illustrate our proposed methodology using NSSP water quality standards as an example. While several MPN- and CFU-based FIB analysis procedures are in common use (for a wide range of water body designated uses), the three cited in NSSP-recommended standards for shellfish growing waters (see ref (11), Chapter 2, Subsection IV.02) are the 5-tube multiple tube fermentation (MTF), the 3-tube MTF, and the membrane filtration (MF) procedure for fecal coliform bacteria. Here, we explore only the 5-tube MTF and the MF procedures because they are far more common than the 3-tube MTF procedure. The standard 5-tube MTF procedure involves diluting a water quality sample into 3 sets of 5 tubes, with each set of 5 containing either 10 mL, 1 mL, or 0.1 mL of the original sample (alternative dilutions may be used depending on the expected concentration of the sample (15)). The MPN is then the maximum likelihood estimate (MLE) of the true fecal coliform concentration based on the number of positive tubes observed in each dilution series after a period of incubation (15–18). A positive tube is one containing visible gas, which serves as an indication of bacterial lactose fermentation. The MF procedure involves filtering a water quality sample and counting the number of bacteria colonies emerging from the filter on a growth plate after a period of incubation. The number of colonies is divided by the sample aliquot volume and reported as the CFU (19–23). MPN and CFU values are intrinsically variable and subject to additional uncertainty arising from minor variations in experimental protocol. NSSP criteria address MPN and CFU variability by recommending that a water body assessment be based on a minimum number n of MPN or CFU values, and by recommending separate numeric standards for the median, geometric mean, and 90th percentile of those values (Table 1). For example, the NSSP criteria for MPN values from a standard 5-tube MTF decimal dilution analysis state that a growing area is classified as “Approved” if a “minimum of 30 of the most recent randomly collected samples” have an MPN median and geometric mean no greater than 14 organisms per 100 mL, and an estimated MPN 90th percentile no greater than 43 organisms per 100 mL (11). Ninetieth percentiles are calculated from a log-normal distribution parametrized by the mean and variance of the natural logarithm of the n MPN or CFU values (11). A common goal of model-based TMDL assessments is to evaluate pollution loading mitigation strategies which will result in compliance with water quality standards. Despite a growing body of research on the role of models and model uncertainty in water resources management (7, 14, 24), we know of no water quality models which explicitly acknowledge how natural variability in FIB concentrations, combined with intrinsic analytic uncertainty, propagates into MPN- or
Most water quality standards, including those based on FIB concentrations, imply that long-term pollutant concentrations at a monitoring station are adequately characterized by an assumed stationary log-normal probability distribution (6, 13). The 30 fecal coliform samples required by NSSP guidelines, however, are usually collected at bimonthly intervals, implying that shellfish harvesting area water quality assessments may take 4-5 years to complete. Changes in fecal coliform sources and delivery routes during that time are likely to translate into changes in the fecal coliform concentration distribution. Here, we assume a constant fecal coliform concentration probability distribution at a monitoring station throughout the assessment period. While we recognize this is a potentially restrictive assumption, it is consistent with current management practice and allows our results to be easily compared with recommended water quality criteria. Developing strategies for assessing a water body based on a changing pollutant concentration probability distribution is an area for additional research (25). We also assume that water quality samples are either simulated (as in the case of a model forecast) or collected based on a systematic random sampling program. In other words, we assume that the 30 samples (as required by NSSP guidelines) are collected under environmental conditions (such as rainfall and tide, for example) indicative of longterm distributions. Furthermore, we presume that the NSSP criteria for an “Approved” classification implies compliance with shellfish harvesting area water quality standards in NSSP guidelines, Chapter 2, subsection 02F (“Standards for approved classification of growing areas affected by non-point sources”) (11). 2.1. Translation of Model-Predicted Concentrations to MPN- and CFU-Based Standard Compliance. As a starting point, we assume that uncertainty in a water quality model or variability in the environment leads to a probability distribution on the fecal coliform concentration c (in organisms per 100 mL) that is log-normal, LN(µc, σc), where µc and σc are the mean and standard deviation, respectively, of the natural logarithm of c . Therefore, we began our analysis by simulating 300,000 concentrations drawn at random from this distribution. We then randomly grouped the 300,000 simulations into 10,000 “samples” of size 30. We repeated the simulation for values of µc evenly spaced between 0 and 3.5 in log(organisms per 100 mL) (at intervals of 0.05), and values of σc evenly spaced between 0 and 3.0 in log(organisms per 100 mL) (at intervals of 0.1), and all combinations thereof. The ranges of values for µc and σc were selected based on a preliminary analysis of MPN values from the Newport River Estuary. For each of the 300,000 fecal coliform concentration values, we randomly drew an MPN and a CFU value from the conditional sampling distribution. For the MPN values, weusedaPoisson/binomialprobabilitymodel(12,15,16,26–31) written as pi ) 1 - e-cvi⁄100
[∏ d
MPN ) argmax c
i)1
pixi(1 - pi)mi-xi
(1)
]
(2)
where pi ) probability of a positive tube in dilution series i, c ) fecal coliform concentration (in organisms per 100 mL), vi ) volume of original sample in dilution series i (mL), d ) number of dilution series (often 3), xi ) number of positive tubes in dilution series i (i [1,. . .,d]), and mi ) number of tubes in dilution series i (often 5). VOL. 42, NO. 13, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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FIGURE 1. Combinations of the mean µc and standard deviation σc of the log-transformed fecal coliform concentration distribution which yielded MPN (solid lines) or CFU (dotted lines) samples in violation of the NSSP median standard (panel a), geometric mean standard (panel b), 90th percentile standard (panel c), or any standard (panel d) with a frequency of either 0.005 or 0.1. The zone of violations is in the upper right of each panel. CFU values were generated using a Poisson Po(λ) probability model (32): λ ) cV ⁄ 100 y|λ ∼ Po(y|λ) ) λye-λ ⁄ y!
(3)
CFU ) 100y ⁄ V
(4)
where y ) number of identifiable colony forming units, and V ) sample aliquot volume. Previous authors have suggested that the Poisson distribution underestimates the variability of microorganisms in both natural waters and sample aliquots and recommend using the negative binomial distribution instead (32–37). However, the Poisson probabilities in our eqs 1 and 3 represent only the conditional probabilities of positive tubes and CFU values given the true fecal coliform concentration c . Because we also assume a log-normal distribution on c, the marginal distributions of positive tubes and CFU values are very similar to the negative binomial. It is possible, however, that the conditional distributions represented by eqs 1 and 3 may also be more widely dispersed than Poisson due to departures in laboratory procedure from standard protocol, clumping of bacteria cells, and similar issues (34, 38). We explored probability models more dispersed than the Poisson and found that our analysis would only change significantly if the methodological variability (e.g., measurement error, cell damage, filter bypass) were 33% greater than that described by the Poisson distribution (see Supporting 4678
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Information for details). We believe that variability of this magnitude is highly unlikely when standard laboratory procedures are carefully followed. For each (µc, σc) pair, we recorded the proportion of the 10,000 simulated size-30 samples which violated the geometric mean standard, the median standard, the 90th percentile standard, or any of the three standards for both MPN and CFU values (see Table 1). Simulations and calculations were performed using the statistics and graphics software program R (39). 2.2. Determination of Concentration-Based Standards. Guidelines prepared by USEPA for assessing water quality impairment suggest that a waterbody does not support its designated use if 10% of samples violate associated designated use criteria (40, 41). NSSP guidelines for shellfish harvesting waters address this provision by setting numeric limits on statistics of a set of at least 30 consecutive water quality samples. According to NSSP guidelines, any size-30 sample which violates any of the standards (i.e., geometric mean, median, or 90th percentile) indicates impairment. Given our probabilistic framework, however, it is effectively impossible to obtain a predicted fecal coliform concentration distribution that will violate standards with zero probability. We therefore identified (µc, σc) pairs that would violate standards no more than 0.5% of the time. We also identified those pairs violating standards no more than 10% of the time for purposes of comparison.
To formulate our results in the form of a more readily implementable regulatory standard, we statistically estimated the equation of the line in (µc, σc) space that divides violating from nonviolating concentration distributions. This was done by fitting a regression model to points on the violation boundary (see Supporting Information for details). 2.3. Translation of MPN and CFU Values to Concentration-Based Standard Compliance. Assessing compliance with concentration-based standards from traditional MPN and CFU observations requires “reversing” the logic of the probabilistic expressions given in eqs 2, 3, and 4 through a process of Bayesian inference (42, 43). This involves using these equations, together with the log-normal distribution on c, as the likelihood functions for µc and σc and then multiplying these likelihoods by prior distributions on µc and σc. Following approaches of refs 44–47, we use diffuse prior distributions for µc and σc in the model of J independent observations of the concentration c at a given monitoring station: cj |µc, σc iid ∼ LN(cj|µc, σc), j ) 1, . . ., J µc ∼ Normal(µ0 ) 0, σc ) 1 000 000) σc ∼ Uniform(lower ) 0, upper ) 100)
(5)
We then implemented a Markov-chain Monte Carlo (MCMC) procedure to generate samples from the joint (µc, σc) posterior distribution using the Bayesian software package WinBUGS (48). Posterior distributions used in our analysis are based on 1000 MCMC samples collected after convergence, as ˆ ) 1.0 (44). indicated by a potential scale reduction factor R Although we used very diffuse priors in this analysis, the Bayesian approach is still preferable to a frequentist method because it yields a full posterior distribution for the distributional parameters, rather than mere point estimates. This allows us to express our results in terms of both “confidence of compliance” (6, 31) and in terms of the posterior probability of a sample of size n revealing a violation. We define confidence of compliance (CC) in this case as the posterior probability that the actual values of µc and σc are below our proposed violation boundaries. We estimated CC by integrating the joint (µc, σc) posterior probability density function over all possible µc and σc values that fall below these boundaries. The posterior probability of a sample revealing a violation is estimated by using MCMC samples from the full joint (µc, σc) posterior distribution to generate samples of fecal coliform concentration from the log-normal distribution. These concentrations are then propagated through eqs 1 and 2 to generate size-30 sample sets of MPN values, from which violation probabilities can be calculated. 2.4. Application to the Newport River Estuary. We applied our Bayesian inference procedure and concentrationbased (µc, σc) standards to water quality monitoring data collected from the Newport River Estuary, NC, during the most recent assessment period (2000-2005). The NC Department of Environment and Natural Resources, Shellfish Sanitation and Recreational Water Quality Section (NCDENRSSS) collects ambient fecal coliform samples from this estuary (and other shellfish harvesting waters throughout North Carolina) at roughly bimonthly intervals and analyzes each sample using the 5-tube MTF procedure. The Newport River Estuary is historically a productive shellfish harvesting area. However, all of its segments and tributaries are either permanently or conditionally closed to shellfishing based on poor water quality or proximity to known or potential sources of fecal contamination. As a result, the estuary and its tributaries comprise 28 of the designated shellfish harvesting areas in North Carolina which are currently included in the USEPA 303(d) list and therefore require a TMDL assessment. Our goal in analyzing these data is to determine whether our concentration-based approach would
have yielded a different impairment decision than that obtained using the MPN-based standard, and therefore whether water quality data provide quantitative support for including the Newport River (and its tributaries) on the 303(d) list.
3. Results 3.1. Data Simulations. Simulation results indicate that (for a given µc and σc) samples will violate NSSP water quality standards at different frequencies depending on whether they are assessed using the MPN-based standard or the CFUbased standard (Figure 1). Additionally, the relative stringency of the two standards will depend on the value of σc. Specifically, application of the 5-tube MTF procedure (and associated MPN standard) to a particular sample is less likely to lead to a violation than application of the MF procedure (and CFU standard) when σc is greater than 0.65, and more likely to lead to a violation when σc is less than 0.65 (Figure 1d). Results also indicate that samples with values in the range of those collected at the Newport River shellfish harvesting area monitoring stations are more likely to be in violation of the NSSP 90th percentile standards (Figure 1c) than either the median or geometric mean standards (Figure 1a and b). 3.2. Concentration-Based Standards. Our regressionbased estimation of the lines that divide violating from nonviolating values in the joint (µc, σc) space reveals that “compliant” values of µc and σc (i.e., those expected to violate any of the three MPN or CFU-based standards no more than 0.5% of the time) are defined by the following inequalities for the MPN procedure:
{
2.65 - σc1.39 1.04 µc e 2.44 - σ2.61 c 1.05
for σc > 0.65 for σc e 0.65
and by the following inequalities for the CFU procedure:
{
1.98 - σc1.03 for σc > 0.65 0.66 µc e 2.35 1.65 - σc for σc e 0.65 0.66 Thus, with point estimates of µc and σc determined for a particular site from either a simulation model or samplebased inference procedure, the frequency-based compliance status of that site can be established in a straightforward way. Of course, when there is uncertainty about µc and σc, then, rather than a binary compliance determination, a CC is the result, as demonstrated in the next section. 3.3. Newport River Estuary Assessment. Application of our concentration-based assessment to the MPN data of the Newport River Estuary resulted in eight stations having an assessed CC less than 1%, whether employing the NSSP MPN or CFU standard (Table 2). Samples collected between 2000 and 2005 actually revealed MPN standard violations at all eight of these stations. While violations were not found at any of the other stations during this period, our Bayesian inference procedure indicates a low CC with the MPN standard (less than 25%) at four other stations as well (Stns. 8, 8A, 25, and 84). This reflects the stringency of the NSSP guideline that no violations, ever, will be tolerated (which we operationalized as a violation frequency of less than 0.5%). Thus, a station such as station 25, which did not actually reveal a violation during the 2000-2005 assessment period, still has a pattern of MPN values that indicate it would be highly unlikely (3% probability) to comply with the standard if enough samples were collected. On the other hand, we can VOL. 42, NO. 13, 2008 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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TABLE 2. Estimated Confidence of Compliance (CC), Posterior Probability of Violating any MPN Standard, and Observed Violations for Monitoring Stations in the Newport River Estuary during the 2000-2005 Assessment Period CC (%) station MPN 3 4 4A 4B 5A 7 8 8A 9 10 11 14A 16A 18 24 25 27A 28 29 35 41 41A 55 56 83 84 85 86
52 44
